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Developability conditions for prestress optimization of a curved surface

机译：曲面预应力优化的可开发性条件

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摘要

Developability conditions are presented for prestressed curved surfaces to be reduced to plane sheets by relaxing the stresses. Those conditions are applied to an optimization problem for minimizing the deviation of stresses from the target values. Two formulations based on the displacements defined by the local and global coordinates of finite elements are presented. It is shown that the numbers of constraints by those formulations are same if triangular elements are used, and there is an upper bound in the number of the elements in a cutting sheet. Performances of the two formulations are compared in the numerical examples, and the local formulation is shown to lead to more accurate estimation of stresses that are actually generated by connecting and stretching the plane sheets.
机译：提出了通过松弛应力将预应力曲面减小为平面的可开发性条件。将这些条件应用于最优化问题，以使应力与目标值的偏差最小。提出了两种基于有限元局部和整体坐标定义的位移的公式。结果表明，如果使用三角形元素，这些公式的约束数量是相同的，并且在裁切纸中元素的数量存在上限。在数值示例中比较了两种配方的性能，并显示了局部配方可导致对连接和拉伸平面片实际产生的应力进行更准确的估算。

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